Abstract
Culling of infected individuals is a widely used measure for the control of several plant and animal pathogens but culling first requires detection of often cryptically-infected hosts. In this paper, we address the problem of how to allocate resources between detection and culling when the budget for disease management is limited. The results are generic but we motivate the problem for the control of a botanical epidemic in a natural ecosystem: sudden oak death in mixed evergreen forests in coastal California, in which species composition is generally dominated by a spreader species (bay laurel) and a second host species (coast live oak) that is an epidemiological dead-end in that it does not transmit infection but which is frequently a target for preservation. Using a combination of an epidemiological model for two host species with a common pathogen together with optimal control theory we address the problem of how to balance the allocation of resources for detection and epidemic control in order to preserve both host species in the ecosystem. Contrary to simple expectations our results show that an intermediate level of detection is optimal. Low levels of detection, characteristic of low effort expended on searching and detection of diseased trees, and high detection levels, exemplified by the deployment of large amounts of resources to identify diseased trees, fail to bring the epidemic under control. Importantly, we show that a slight change in the balance between the resources allocated to detection and those allocated to control may lead to drastic inefficiencies in control strategies. The results hold when quarantine is introduced to reduce the ingress of infected material into the region of interest.
Highlights
There is increasing interest in coupling epidemiological with economic models in order to identify optimal strategies for disease control [1,2,3,4,5]
We have used an SI-X metapopulation model to describe the dynamics of an epidemic spreading on a two-species host community in which there is a spreader host and a target species that we wish to preserve
In considering culling in the absence of quarantine, we have proved, analytically, that the optimal culling strategy involves removal of as many detected individuals as possible, in the spreader species driving the epidemic
Summary
There is increasing interest in coupling epidemiological with economic models in order to identify optimal strategies for disease control [1,2,3,4,5]. Sethi [6] and others [7,8,9] first used optimal control theory to identify optimal strategies for disease control under a range of simplified epidemiological scenarios. Our principal objective is to identify optimal culling strategies for disease control and to investigate how limited resources should be balanced between disease detection and eradication in order to maximize the effectiveness of the control policy. We define eradication in the sense frequently used in plant disease epidemiology as reducing the rate of production of inoculum during the course of the epidemic by destroying the sources of inoculum (culling) [14,15]
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